nLab triple category

Triple categories

Triple categories


A triple category is an n-fold category for n=3n=3. That is, it is an internal category in double categories. This concept can be considered at various levels of strictness. However, there is not yet a definition in the literature of a fully weak (i.e. pseudo) triple category.


  • strict triple category?
  • intercategory
  • The double category of algebras can be enhanced to a triple category
  • Just as any category gives rise to a double category of commutative squares, any double category gives rise to a triple category of commutative “cubes” by taking the transversal morphisms to be the same as the vertical morphisms.

Last revised on July 28, 2023 at 14:25:06. See the history of this page for a list of all contributions to it.